2. A LabVIEW Data Acquisition System VI 16
A.1 Data Acquisition Controller.vi . . . . . . . . . . . . . . . . . . . . . . . . 16
A.2 host.vi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
B Flutter Point Computation Matlab Code 19
C Ultra Nano Servo HS-35HD 20
D Control Surface Design Details 21
E Connect PXIe-8133 Controller to Host Computer 23
2
3. 1 Introduction
The goal of the independent study is to learn basic concepts in aeroelasticity through
experiments. The main tasks for the project are setting up experiments for divergence,
flutter and aeroelastic control in a 30cm × 30cm wind tunnel. Data acquisition system is
also needed to provide data for theory validation.
2 Wind Tunnel Setup
2.1 Model Selection
Since flutter phenomenon should be observed, the model should present dynamic
aeroelasticity properties, which are the intersection of elasticity, dynamics, and aeroelas-
ticity. And limited by the size of the wind tunnel (30cm × 30cm), the elastic property
of the airfoil has little effect in the experiment and could be assume as a rigid body. So
with the leading edge of the airfoil facing the entrance of wind tunnel and staying hori-
zontally, only pitch and plunge motions are expected during the experiment. Therefore,
typical-section model is selected (Fig. 1).
Figure 1: Schematic drawing of a typical-section model
To provide a torsional stiffness and tensile stiffness at the same time, eight springs
are used in this model, four on top of the airfoil and four at the bottom. The stiffness of
the eight springs are the same. And some foam is removed from the airfoil to keep the
center of gravity at the middle of the chord. The elastic center of the airfoil is also at the
midpoint of its chord. The original set up is shown in Figure 2. The parameters of the
airfoil and springs are listed in Table 1.
2.2 Components Design
2.2.1 Spring Attachment
The attachment component for springs on airfoil should be light. And the attachment
on both airfoil and wind tunnel should provide multiple connect positions for springs.
With the requirements above, the final design of the attachment componene is shown in
3
4. Figure 2: Original wind tunnel set up
Table 1: Airfoil model parameters
Item (units) Value
Airfoil NACA 0012
Span(mm) 290
Chord (mm) 110
Mass (g) 56.2
Spring constant (kg/m) 15.24
spring original length (mm) 107.0
Figure 3. The spacing between two hooks is tenth of chord length, which is 1.1 cm. The
hooks are numbered from 1 on leading edge to 10 on trailing edge. The hooks are stick
out from a plastic sheet. The thickness of the sheet is carefully designed to maintain the
strength as well as keep it flexible enough to adhere to the curvature of the airfoil. These
pieces are stuck to the object using epoxy.
2.2.2 Restrict Rod (for Divergence Experiment Only)
For divergence experiment, which is a static aeroelasticity phenomenon, the motion
of the airfoil is expected to be constrained to only rotation and plunge, the displacement
in horizontal direction is not desired. So the pair of rods (Fig. 4) is design to insert to
the center hole of the airfoil to limit its motion. The total mass for these two parts is 6.2
g.
4
5. (a) Airfoil spring attachment (b) Wind tunnel spring attachment
Figure 3: Spring attachment design CAD
Figure 4: Restrict rod CAD
3 Divergence Experiment
3.1 Divergence Phenomenon
Divergence is one of the important phenomenon in static aeroelasticity. It is a static
instability of the lifting-surface structure, which could results in catastrophe failure. Di-
vergence occurs when the lifting surface deforms due to its aerodynamics loads, and the
deformation of the structure further increases the loads, which deflects the structure fur-
ther. This vicious circle ends when a failure occurs. The coupled aerodynamics force and
structure elasticity decrease the effective stiffness of the whole system. ([1])
In this experiment, an increasing angle of attack is expected to observed to determine
whether it is divergence or not. The divergence limit speed is measured in the wind
tunnel and also calculated by the theory with the model parameters. In ideal case, these
two values should be close. And an discussion on these two values are carried out.
3.2 Governing Equations
The moment equilibrium is:
Mac + L(xO − xac) − W(xO − xcg) − kθ = 0 (1)
⇒ θ =
qScCMac + qSCLαα(xO − xac) − W(xO − xcg)
k − qSCLα(xO − xac)
(2)
5
6. Figure 5: Divergence model
In order to have divergence occur, the effective stiffness of the structure should vanish,
which means the denominator of θ expression should be zero.
qD =
k
SCLα(xO − xac)
(3)
⇒ UD =
s
2k
ρ∞SCLα(xO − xac)
(4)
Because dynamic pressure should be positive and finite to have physical sense, xO −xac >
0, the aerodynamics center must be in front of the elastic center.
3.3 Experiment
The wind tunnel maximum available air speed is 20.3 mph (9.1 m/s). So the di-
vergence speed calculated by Eqn. 4 should be lower than this limit. By changing the
position of the springs on airfoil, the numerator of Eqn. 4 is varying. And by inserting
mass in the front hole of the airfoil, the elastic center position is changing.
The final positions of the springs are at 0.3c and 0.7c. So the torsional stiffness of the
model is:
kθ = 4khd2
front + 4khd2
rear (5)
= 4 × 15.24 × 0.0112
+ 4 × 15.24 × 0.0112
(6)
= 0.01475Nm/radian (7)
And a total mass of 65.6 g is inserted into the front hole. So the new cg location is:
x0
cg =
mairfoil ∗ xcg + madd ∗ xhole
mairfoil + madd
(8)
=
65.2 × 0.055 + 59.4 × 0.0275
124.6
(9)
= 0.0392m (10)
6
7. And the divergence speed calculated by Eqn. 4 is:
UD =
s
2 × 0.01475
1.220 × (0.29 × 0.11) × 3.86 × (0.0392 − 0.11/4)
(11)
= 4.132m/s(= 9.243mph) (12)
The actual measured value for this experiment is 6.57 m/s. The calculated value is a
little far from the actual value. The possible reasons for the difference are:
1. The model is only restricted in horizontal motion. It can still have little plunge
motion, which makes different to the ideal model.
2. The friction between the rods and the wind tunnel wall change the effective stiffness.
4 Flutter Experiment
4.1 Flutter Phenomenon
Flutter is one of the phenomena in dynamic aeroelasticity. It is a self-excited and
potentially destructive oscillatory instability. The cause of this unstable oscillation is the
aerodynamic forces on a flexible body couple with its natural modes of vibration. The
amplitude would keep increasing until structure failure happens. Because flutter is an
intersection of elasticity, dynamics and aerodynamics, in complex cases, only through
testing can predict and eliminate flutter. ([2])
So to simplify the problem, a typical section model with two degrees of freedom is
applied here. (Section 2.1) With steady air flow in the wind tunnel, the disturbances in
aerodynamics is minimized in this set up.
Oscillations in plunge and pitch motions are expected to be observed. The frequencies
of these two motions should be close enough to distinguish the true flutter phenomenon
from stall flutter. The frequency of flutter is recorded through a data acquisition system
and calculated by a Matlab code. The data come from two accelerometers on leading
edge and trailing edge of the airfoil. The actual wind tunnel setup is shown in Figure 6.
Then, a discussion on these results is carried out.
4.2 Data Acquisition System
4.2.1 NI Data Acquisition Device
A complete NI data acquisition device, which includes a controller and multiple mod-
ula, is used in this experiment. The controller is NI PXIe-8133. It is a powerful computer
itself with labVIEW real-time software installed. All the data collected by modula is col-
lected by the controller and then transmit to a host computer. The modular being used
to collect voltage inputs is PXI-4462, 4-Input Dynamic Signal Analyzer. For detailed
information on the devices, see Ref. [3] for controller, and Ref.[4] for the modular. For
how to connect the controller with a host computer, see Appendix E.
7
8. Figure 6: Flutter experiment wind tunnel setup
4.2.2 LabVIEW VI
A LABVIEW VI is built to work with the NI data acquisition device. The VI should
be capable of collecting analog voltage signals from two accelerometers, implementing
manipulation on the data, and recorded the operated data together with the raw data.
And it should have screens like an oscilloscope to show the real-time waveforms of the
signal.
Since a combination of a controller and a host computer is used here, the VI is a little
different with reading signal on a single computer. A real-time project should first be
generated. In Project Explorer, under the project name, there should be two items in
the sub tree, ”My computer” and ”NI-PXIe8133-2F12EB47”. Under each of these two
subtree are the VI on itself, which means VIs would run separately on controller and host
computer. The data is transferred between them through the global variables shown in
the Project Explorer. So a VI would run on the controller to collect data, and another
host VI would get the signal through global variable, do manipulation with the data and
record the data on the host computer.
There is a real-time project with two VIs developed for this particular flutter exper-
iment. ”DataAcquisition Controller.vi” is run on controller to collect data. ”host.vi”
is run on host computer to manipulate data and record them on host computer. To
run collect data, first run ”DataAcquisition Controller.vi”, then run ”host.vi”. The data
is recorded on the ”DATA.txt” file on the desktop as soon as host.vi starts, and stop
recorded data as it stops. More detailed descriptions of the VI are in Appendix A.
8
9. 4.3 Governing Equations
Linear aeroelastic system is considered in this experiment. The schematic drawing of
the model is shown in Figure 1. The equations of motion are formulated from Lagrange’s
equations.
For potential energy, it is the sum of the elastic energy in springs.
P =
1
2
khh2
+
1
2
kθθ2
(13)
For kinetic energy, the velocity of the center of gravity is first deduced.
~
VC = −ḣî2 + bθ̇(a − e)b̂2 (14)
K =
1
2
m~
VC · ~
VC +
1
2
ICθ̇2
(15)
⇒ K =
1
2
m(ḣ2
+ 2bxθḣθ̇) +
1
2
Ipθ̇2
(16)
where Ip = IC + mb2
x2
θ.
And generalized forces on the right side of Lagrange’s equations are:
Qh = −L (17)
Qθ = M1
4
+ b
1
2
+ a
L (18)
Inserting into the Lagrange’s equation:
m(ḧ + bxθθ̈) + khh = −L (19)
Ipθ̈ + mbxθḧ + kθθ = M1
4
+ b(
1
2
+ b)L (20)
L = ρ∞bU2
θCLα (21)
M1
4
= 0 (22)
p method is applied here to solve the equations. To simplify the notation of the equations,
natural frequencies of pitch and plunge, and several dimensionless parameters are used.
ωh =
r
kh
m
(23)
ωθ =
s
kθ
Ip
(24)
r2
=
Ip
mb2
(25)
σ =
ωh
ωtheta
(26)
µ =
2m
ρ∞CLαb2
(27)
V =
U
bωθ
(28)
9
10. and let v = pU
b
the equations are simplified to matrix form of:
p2
+ a2
V 2 xθp2
+ 1
µ
xθp2
r2
p2
+ r2
V 2 − 1
µ
(a + 1
2
)
# h̄
b
θ̄
=
0
0
(29)
For a nontrivial solution to exist, the determinant of the coefficient matrix must be zero.
So by solving this, the solutions of p are found.
p1 =
bv1
U
=
b
U
(Γ1 ± iΩ1) (30)
p2 =
bv2
U
=
b
U
(Γ2 ± iΩ2) (31)
At flutter point, the system becomes unstable and has divergent oscillations. So the real
part of p, Γk 0, and the imaginary part, Ωk 6= 0. A Matlab code is programmed to do
the calculation and display the varying roots p as airspeed changing. (Appendix B )
4.4 Experiment
4.4.1 Experiment Result
In order to observe flutter phenomenon in the wind tunnel, several parameters should
be carefully set. First, divergence shouldn’t occur before flutter happens, which indicates
the cg should push backwards. If necessary, addition mass could be attached to the
leading edge of the airfoil. Second, the flutter limit speed should be within the speed
range of the wind tunnel, this could be achieved by adjusting the spacing of springs on
the airfoil to change the effective stiffness of the whole system. And finally, stall flutter
is not wanted, so the disturbance in air flow should be limited.
The final setup of the whole system are listed in Table 2.
Table 2: Flutter Experiment Setup
Item (units) Value
Airfoil NACA 0012
Span(m) 0.29
Semi-chord (m) 0.055
Mass (kg) 0.0908
Spring constant (kg/m) 15.24
Spring position(from LE) 0.3c, 0.7c
Center of gravity(m from LE) 0.057
Elastic axix (m from LE) 0.055
Air density (kg/m3
) 1.20
Natural frequency of plunge (rad/s) 29.84
Natural frequency of pitch (rad/s) 41.43
With this setup, flutter is observed, and the wave diagrams of pitch and plunge motion
are shown in Figure 7. The airspeed at the flutter point is 7.9 mph (3.53 m/s). And the
flutter frequency is 4.85 Hz.
10
11. Figure 7: Wave diagram of pitch and plunge motion
4.4.2 Calculated Result
First, the natural frequencies of pitch and plunge should be found. With a 6 g mass
piece in the LE hole, the cg location coincides with the elastic axis. Next, do pure pitch
and plunge test to find the reference natural frequency. Then, with Eqn. 23, the original
moment of inertia about elastic axis is found. Finally, calculate the actual Ip by:
I0
p = Ip +
X
mid2
i (32)
I0
p = 9.566 × 10−6
+ 0.0097 ∗ 0.0552
− 0.006 ∗ (frac0.00552)2
= 3.4371 × 10−5
(33)
where m is the additional mass, and d is the distance from the mass to elastic axis.
Then input all the parameters to the matlab code (Appendix B). The output graph is
shown in Figure 8.
The flutter frequency is (0.7774 × 41.43 = 32.2rad/s =) 5.126 Hz, which is close to the
measured value 4.85 Hz. And the flutter speed is (U = V bωθ = 0.99∗0.055∗41.43 =) 3.25
m/s, which is also close to the measured value 3.53 m/s. So the experiment is successful
and the theory is verified.
5 Aeroelastic Control – Open Loop
5.1 Model Design
The main idea of this experiment is to control the flap at trailing of the airfoil to
avoid flutter in the wind tunnel. The basic model is still typical section model, but with
flap equipped. To design the model, it should go through the following steps.
1. Choose the servo to actuate the control surface
2. Decide the chordwise length and spanwise length of the flap
11
12. Figure 8: Flutter point calculation output
3. Design the control mechanism
4. Calculate the flutter speed for the model, the speed limit should before divergence
speed and within the speed range of the wind tunnel.
5. If the speed result in step 4 does not satisfied the requirement, add some mass to
the model and do step 4 again until it come up with a feasible design.
The servo selected is Hitec HS-35HD, which is an ultra nano servo. It is only 7.6 mm
in thickness and 4.5 g is mass. And it can provide enough torque to rotate the flap. Its
detailed feature is in Appendix C.
The chordwise length is determined to be 0.3c.The thickness of the airfoil at 0.7c is
7.9 mm, which is enough for the servo to be embedded in the airfoil. The spanwise length
is 230 mm and the total span is 290 mm so that the accelerometers could still attaches
to the trailing on left side of the airfoil. The 30 mm margins on both left and right side
are the places to attach mass to change model parameters. And with this flap area, the
additional lift provided by the flap should be enough to stabilize flutter in the wind tunnel.
The control mechanism consists of two arms and a shaft. The servo arm actuates the
shaft, then the shaft pull or push the arm on flap to change its deflection angle. The flap
is connected to the main airfoil by Robart pin hinges. The maximum deflection angle is
± 30 degrees.
The final design is shown in Figure 9. And the parameters of the model is listed in
Table 3. The natural frequency of plunge is calculated by Equation 23. The natural
frequency of pitch is derived from Equation 23 and 32. the The detailed component
designs are in Appendix D.
12
13. Figure 9: Control surface final design
Table 3: Parameters of new model with flap
Item (unit) Value
Airfoil NACA 0012
Span(m) 0.29
Semi-chord (m) 0.055
Total mass (kg) 0.0935
Spring constant (kg/m) 15.24
Spring position(from LE) 0.3c, 0.7c
Center of gravity(m from LE) 0.0574
Elastic axix (m from LE) 0.055
Air density (kg/m3
) 1.20
Natural frequency of plunge (rad/s) 29.41
Natural frequency of pitch (rad/s) 44.93
5.2 Flutter Point Estimation
The process to estimate the flutter point with no flap deflection angle is similar in
Section 4.4.2. The inputs of the Matlab code (Appendix B) are in Table 3. And the final
result is shown in Figure 10.
The flutter frequency is (0.7332 × 44.93 = 32.94rad/s =) 5.243 Hz. And the flutter
speed is (U = V bωθ = 0.71 ∗ 0.11 ∗ 44.93 =) 3.509 m/s. So the flutter speed in within the
wind tunnel speed range.
5.3 Effect of Flap
The aerodynamic effect of a flap deployed can be estimated as adding camber to an
airfoil. In our case, with a flap deflection angle, the original symmetric airfoil becomes a
camber one. The camber doesn’t change lift coefficient slope, but it changes the zero-lift
13
14. Figure 10: Flutter point estimate for control model
angle of attack of the airfoil.
Cl = Clα(A0 +
1
2
A1) (34)
= Clα(α +
1
π
Z π
0
dzc
dx
(cos(θ0) − 1)dθ0 (35)
where x is substituted by c
2
(1 − cos(θ0)), θ0 ∈ [0, π]. The chordwise length of the flap is
0.3c, so at x = 0.7c, θ0 = arccos(−0.4), and express the flap deflection angle as β. So
αl0 = −
1
π
Z π
0
dzc
dx
(1 − cos(θ0))dθ0
= −
1
π
Z π
arccos(−0.4)
tan(β)(1 − cos(θ0))dθ0
= −0.661 tan(β)
5.4 Open Loop Control
The deflection of flap provided additional lift to the model, which acts as a damping
force for the flutter. In the open loop control, a fixed accelerometer voltage reading is
set as a trigger. After this limit, the flap will change to a certain angle to stabilize the
model. The actual experiment will be taken as future work to complete this project.
6 Conclusion
During the preparation of experiments for divergence and flutter, the basic knowledge
of aeroelasticity is acquired, especially the governing equations for the coupled system of
14
15. elasticity, aerodynamics and aeroelasticity. And the experience of doing research through
experiment and test is accumulating, from wind tunnel components design, test model
design and evaluation, to LABVIEW programming and operating a data acquisition
system.
7 Future Work
The first future work is to finish the open loop control surface experiment. The actual
model should be built, and the control loop should be programmed in LABVIEW. The
second one is trying to do closed loop control, which can stabilize flutter much faster than
open loop. But this requires an analysis on system delay, especially on servo, and also,
the algorithm is much more complex.
15
16. Appendix A LabVIEW Data Acquisition System VI
A.1 Data Acquisition Controller.vi
This VI is run in controller PXIe-8133. Its front panel contains two waveform screens
to show the signals from accelerometers on LE and TE separately.
Figure 11: Front Panel of Data Acquisition Controller.vi
DAQmx functions in LabVIEW works perfectly with the PXI system. The implement of
the VI is achieved by using DAQmx functions.
Figure 12: Block diagram of Data Acquisition Controller.vi
16
17. A.2 host.vi
The two screens on top show the actual signals from controller. The bottom two
screens show manipulated data waveform. The left one does difference between the
voltage from LE and TE, which represents the pitch motion. The right one calculates
the average of the two voltages, which represents the plunge motion.
Figure 13: Front Panel of host.vi
Data are abstracted from global variables ”LE” and ”TE” 50 times every half seconds,
which means the sample frequency is 100 Hz. Since the estimated flutter frequency is
below 30 Hz, this sample rate is sufficient. The sample output file ”DATA.txt” is:
Time(s) LE (V) TE (V) Pitch(V) Plunge (V)
0 2.692475 2.893949 -0.20147 2.793212
0.01 2.680116 2.889183 -0.20907 2.784649
... ... ... ... ...
17
20. Appendix C Ultra Nano Servo HS-35HD
From http://hitecrcd.com/products/servos/micro-and-mini-servos/analog-micro-and-mi
hs-35hd-ultra-nano-servo/product
20
21. Appendix D Control Surface Design Details
135.39
290
110
230
30
33
30.54
5
10.50
5.86
18
18
Figure 15: Control model three-side view
21
22. Table 4: Control model detail data
Item (unit) Value
Airfoil NACA 0012
Span(m) 0.29
Semi-chord (m) 0.055
Spring constant (kg/m) 15.24
Spring position(from LE) 0.3c, 0.7c
Center of gravity(m from LE) 0.0574
Elastic axix (m from LE) 0.055
Air density (kg/m3
) 1.20
Natural frequency of plunge (rad/s) 29.41
Natural frequency of pitch (rad/s) 44.93
Airfoil mass (kg) 0.059
Spring mass (kg) 0.0144 (0.0018 each)
Accelerometer mass (kg) 0.0024 (0.0012 each)
Servo (kg) 0.0045
Balanced mass on TE (kg) 0.008
Hinges (kg) 0.002 (0.0005 each)
Wire (kg) 3.2
Total mass (kg) 0.0935
22
23. Appendix E Connect PXIe-8133 Controller to Host
Computer
How to Connect PXIe-8133 Controller to a Host Computer
1. First, do some basic check
The PXIe-8133 controller is directly connected to the computer
through a crossover Ethernet cable
Make sure the cable is insert in the Ethernet Port 1 (Port 2 is
disabled)
Boot up the PXIe-8133 controller
2. Go to the right bottom of the screen, click on the internet and select “Open
Network and Sharing center”.
3. Select “Local Area Connection 2” for the unidentified network
4. Click on “Properties”, and select “Internet protocol Version 4(TCP/IPv4)”,
then click on “Properties”.
23
24. 5. Type in the information as shown on the picture below. The IP address for
the PXIe-8133 controller is 169.254.26.217.
25. 6. Open MAX (Measurement Automation Explorer), and expand “Remote
System” sub tree. The “NI-PXIe8133-2F12EB47” should appear below.
26. References
[1] Dewey H. Hodges Introduction to Sructural Dynamics and Aeroelasticity, Seconf Edi-
tion 2002: Cambridg University Press, N.Y.
[2] Earl H.Dowell A Modern Course in Aeroelasticity, Fourth Edition 2004: Kluwer Aca-
demic Publishers, N.Y.
[3] National Instruments, PXI Express, NI PXIe-8133 User Manual http://www.ni.
com/pdf/manuals/372870d.pdf
[4] National Instruments, NI Dynamic Signal Acquisiton User Manual http://www.ni.
com/pdf/manuals/371235h.pdf
26
